2 Write the equation of a line that is perpendicular to y = -5x -8 and passes through the point (0,9) Write the equation of a line that is parallel to y = 4 5 𝑥+13 and passes through the point (0,-6)
3 Chapter 8.9 system of linear equations Today’s objectives: - solve a system of linear equations through graphing and determine whether there is one solution, infinite solutions, or no solution.
4 Important vocabulary System of linear equations -two linear equations with the same two variables. The two variables will make both equations true.ex: 2x -1 = y **the solution x = 5 and y = 9 makesx + 4 = y both statements true.Solution of a linear system- an ordered pair (x,y) whose values make both linear equations true.
5 We can graph two linear equations to find a solution… Y = 2x – 4 Y = -3x + 1
6 We can graph two linear equations to find a solution… Y = x + 2 Y = -2x + 2
7 We can graph two linear equations to find a solution… Y = x + 4 Y = 4x + 1
8 There can be 3 different outcomes to graphing a system of linear equations…
9 Find the solution to the system y + 2x = 1 y = -2x + 3
10 Find the solution to the system y x = 5 y = x + 5
11 Find the solution to the system Y = 1 2 x + 2 Y = -x + 5
12 Steps we take to solve a system by graphing 1.) make sure both equations are in slope-intercept form y = mx + b 2.) graph both equations 3.) find the solution -three different outcomes 1- one solution 2- infinite solutions 3 - no solution
13 Practice on your own1.) y = 1 3 𝑥 – 3 2.) y – x = 5 3.) y 𝑥 = 2 y = 𝑥 + 1 y = x + 7 y – 2 = 2 3 𝑥